Find the intersection

Question

y = -x^2 and y = x^2 - 4x + 4

Answer 1

-x^2 = x^2 -4x +4

2x^2 -4x +4 =0

x^2 -2x +2 = 0

x = 2/2 +/-sqr(4-4(2))

x = 1 +/-2i

x = 1+2i or 1-2i

first is a downward opening parabola

2nd is an upward opening parabola

they never intersect, except in imaginary numbers